Bivariate splines for ozone concentration predictions

For ground level ozone prediction, we consider a functional linearregression model where the explanatory variable is a real randomsurface and the response is a real random variable. We use bivariatesplines over triangulations to represent the random surfaces. Then weuse this representation to construct two solutions, a least squares estimate of the regression function based on a brute force approach, and an autoregressive estimator based on a principal component analysis. Weapply these two functional linear models to ground level ozone forecasting over the United States to illustrate the predictive skills of these two methods. We also extend the brute force approach to a model where both the explanatory variable and the response are both real random surfaces.